University of TabrizComputational Methods for Differential Equations2345-39823220150401Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation70864017ENMinaMortazaviDepartment of Applied Mathematics,
School of Mathematical Sciences,
Ferdowsi University of Mashhad,
Mashhad, IranMohammadMirzazadehDepartment of Mathematics,
Faculty of Mathematical Sciences,
University of Guilan, Rasht, IranJournal Article20141205In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by jacobi elliptic functions for the 1D MCGL equation are derived. Homogeneous method is a powerful method, it can be used to construct a large families of exact solutions to different nonlinear differential equations that does not involve independent variables.https://cmde.tabrizu.ac.ir/article_4017_0464648f9f5a70082b84fd3112ca2dcf.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823220150401Optimization with the time-dependent Navier-Stokes equations as constraints87984484ENMitraVizhehDepartment of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, IranSyaed HodjatollahMomeni-MasulehDepartment of Mathematics, Shahed University, Tehran, P.O. Box: 18151-159, IranAlaeddinMalekDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, P.O. Box: 14115-134, IranJournal Article20150606In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the optimal control of the Navier-Stokes equations is proposed. Numerical examples are given to demonstrate the efficiency of the method.https://cmde.tabrizu.ac.ir/article_4484_0de495e641081aae07a2b511ceceb9bf.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823220150401Application of the block backward differential formula for numerical solution of Volterra integro-differential equations991004541ENSomayyehFazeliMarand Faculty of Engineering, University of Tabriz, Tabriz-IranJournal Article20151017In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability region of orders 2, 3 and 4 are constructed which are suitable for solving stiff VIDEs.https://cmde.tabrizu.ac.ir/article_4541_07598b31f5bf268f9053f664f3870864.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823220150401Numerical solution of time-dependent foam drainage equation (FDE)1111224648ENMuratGubesKaramanoglu Mehmetbey University, Department of Mathematics,Yunus Emre Campus,
70100, Karaman / TurkeyYildirayKeskinSelcuk University, Department of Mathematics, Alaaddin Keykubat Campus, 42030, Konya / TurkeyGalipOturancSelcuk University, Department of Mathematics, Alaaddin Keykubat Campus, 42030, Konya / TurkeyJournal Article20150608Reduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE) with different initial conditions. We compare our method with the famous Adomian Decomposition and Laplace Decomposition Methods. The obtained results demonstrated that RDTM is a powerful tool for solving nonlinear partial differential equations (PDEs), it can be applied very easily and it has less computational work than other existing methods like Adomian decomposition and Laplace decomposition. Additionally, effectiveness and precision of RDTM solutions are shown in tables and graphically.https://cmde.tabrizu.ac.ir/article_4648_efda79e599c82bb21304dce4c2502549.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823220150401Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem1231334649ENRahmatDarziDepartment of Mathematics, Neka Branch,
Islamic Azad University, Neka, IranBahramAgheliDepartment of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IranJournal Article20150914In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0<t<1, 2<alpha<3, x(0)= x'(0)=0, x'(1)=beta x(xi)$, where $D_{0^{+}}^{alpha}$ denotes the standard Riemann-Liouville fractional derivative,$0<xi<1$ and $0<\beta\xi^{\alpha-1}<\alpha-1$ Our analysis relies a fixed point theorem in partially ordered sets. An illustrative example is also presented.https://cmde.tabrizu.ac.ir/article_4649_30ab2f42a41eb1f68dba3f0aab9d34fc.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39823220150401Multi soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)-dimension1341464769ENManjitSinghYadawindra College of Engineering,
Punjabi University Guru Kashi Campus,
Talwandi Sabo-151302, Punjab, IndiaJournal Article20151214As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of associated linear problem or Lax pair are presented in straightforward manner and finally for proposed nonlinear equation, explicit one, two and three soliton solutions are also obtained.https://cmde.tabrizu.ac.ir/article_4769_c037a3bd2246ff1cd130bac4856a2745.pdf